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Popular >

derivative of x^2ln(x^2+1)

Solution

derivative of

x^{2} ln (x^{2} + 1)

Solution

2 x ln (x^{2} + 1) + \frac{2 x ^{3}}{x ^{2} + 1}

Solution steps

\frac{d}{d x} (x^{2} ln (x^{2} + 1))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{2}, g = ln (x^{2} + 1)

= \frac{d}{d x} (x^{2}) ln (x^{2} + 1) + \frac{d}{d x} (ln (x^{2} + 1)) x^{2}

\frac{d}{d x} (x^{2}) = 2 x

\frac{d}{d x} (ln (x^{2} + 1)) = \frac{2 x}{x ^{2} + 1}

= 2 x ln (x^{2} + 1) + \frac{2 x}{x ^{2} + 1} x^{2}

\frac{2 x}{x ^{2} + 1} x^{2} = \frac{2 x ^{3}}{x ^{2} + 1}

= 2 x ln (x^{2} + 1) + \frac{2 x ^{3}}{x ^{2} + 1}

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Frequently Asked Questions (FAQ)

What is the derivative of x^2ln(x^2+1) ?
The derivative of x^2ln(x^2+1) is 2xln(x^2+1)+(2x^3)/(x^2+1)
What is the first derivative of x^2ln(x^2+1) ?
The first derivative of x^2ln(x^2+1) is 2xln(x^2+1)+(2x^3)/(x^2+1)